A note on lattices with many sublattices

2018/12/30 by Czédli, Gábor, Horváth, Eszter K.
#06B99 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1812.11512

Abstract

For every natural number n≥ 5, we prove that the number of subuniverses of an n-element lattice is 2ⁿ, 13⋅ 2^n-4, 23⋅ 2^n-5, or less than 23⋅ 2^n-5. By a subuniverse, we mean a sublattice or the emptyset. Also, we describe the n-element lattices with exactly 2ⁿ, 13⋅ 2^n-4, or 23⋅ 2^n-5 subuniverses.

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